. Railroad construction. Theory and practice. A textbook for the use of students in colleges and technical schools . radius r of the connecting curve from F to S, Fig. 147, and itslength or central angle. In the triangle CSF CS + CF:CS-CF::tsin i(CFS-\rCSF):tm HCFS-CSF); n § 273. SWITCHES AND CROSSINGS. 309 but i(CFS + CSF) =90-i(p; and, since the triangle 0^SF iaisosceles, i(CFS -CSF) = ^F; .-. 2R + d:d-g::cot i^:tan ^F::cot JF:tan i<p; ••• *-i^=-S3^ <io«) From the triangle COiF we may derive r — ig:R-\-ig::sin ^:sin (i^+^); ^-^^ = ^^ + i^)ih^W^- . o . . (110) Also i^6^=2()sinKi^ +
. Railroad construction. Theory and practice. A textbook for the use of students in colleges and technical schools . radius r of the connecting curve from F to S, Fig. 147, and itslength or central angle. In the triangle CSF CS + CF:CS-CF::tsin i(CFS-\rCSF):tm HCFS-CSF); n § 273. SWITCHES AND CROSSINGS. 309 but i(CFS + CSF) =90-i(p; and, since the triangle 0^SF iaisosceles, i(CFS -CSF) = ^F; .-. 2R + d:d-g::cot i^:tan ^F::cot JF:tan i<p; ••• *-i^=-S3^ <io«) From the triangle COiF we may derive r — ig:R-\-ig::sin ^:sin (i^+^); ^-^^ = ^^ + i^)ih^W^- . o . . (110) Also i^6^=2()sinKi^ + ^) (Ill) 273. Connecting curve from a curved track to the Fig. 148. As above, it may readily be deduced from the triangle CFS (seeFig. 148) that (2R-d): (d -g):: cot J^: tan iF,and finally that *-*^-;?:^f (2) Similarly we may derive (as in Eq. 110) (r-i9)HR-i9)^^^y . (113) 310 RAILROAD CONSTRUCTION. §273. Also FS=2(r-ig)smi(F-(P) (114) Two other cases are possible,becomes infinite (see Fig. 149),then F = (lf, In such a casewe may write, by substitut-ing in Eq. 112, 2R-d=\d-g). .(115) This equation shows the valueof Rf which renders this casepossible with the given valuesof n, df and g, (h) (p may begreater than F, As before(see Fig. 150) 2R-d:d-g::cot J^itanji^;the same as Eq. 112, but (a) r may increase until it
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